Related papers: A general framework for Krylov ODE residuals with …

In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO). The key step of RISRO is…

We present a novel Krylov subspace method for approximating $L_f(A, E) \vc{b}$, the matrix-vector product of the Fr\'echet derivative $L_f(A, E)$ of a large-scale matrix function $f(A)$ in direction $E$, a task that arises naturally in the…

In recent years, a great deal of attention has been focused on numerically solving exponential integrators. The important ingredient to the implementation of exponential integrators is the efficient and accurate evaluation of the so called…

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…

Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a…

Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are…

In this work, we propose a reduced basis method for efficient solution of parametric linear systems. The coefficient matrix is assumed to be a linear matrix-valued function that is symmetric and positive definite for admissible values of…

Prior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential ${\rm e}^{tA}v$, is extended to the case of associated $\varphi$-functions (which occur within the class…

We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur…

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel…

We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al.; SISC 2005], which is an iterative method allowing for the efficient minimization of the the residual over an augmented Krylov subspace. We offer a…

This paper develops a new class of exponential-type integrators where all the matrix exponentiations are performed in a single Krylov space of low dimension. The new family, called Lightly Implicit Krylov-Exponential (LIKE), is well suited…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

We develop a randomized extension of tensor Krylov subspace methods based on the Einstein product for solving large-scale multilinear systems arising in image and video restoration. The classical tensor global GMRES method relies on…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the…

We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…

Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive…

With the recent realization of exascale performace by Oak Ridge National Laboratory's Frontier supercomputer, reducing communication in kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods,…

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…